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We introduce spatial operators by a simple example of taking the average value of all pixels in a box surrounding each input pixel. The result is a blurring or smoothing of the input image.

We run into problems when we take all of the pixels in a box around an input pixel and that pixel is close to one of the edges of the image. Let’s look at some strategies to deal with edge pixels.

Taking an average of pixels in a box leads to artefacts such as ringing which we can remedy by taking a weighted average of all the pixels in the box surrounding the input pixel. The set of weights is referred to as a kernel. A common kernel used for image smoothing is the Gaussian kernel.

A problem arises when using three-angle sequences and particular values of the middle angle leads to a condition called a singularity. This mathematical phenomena is related to a problem that occurs in the physical world with mechanical gimbal systems. Note that in Robotics, Vision & Control (second edition) and RTB10.x the default definition of roll-pitch-yaw […]

We learn how to describe the orientation of an object by a 3×3 rotation matrix which has some special properties.

We learn how to describe the 2D pose of an object by a 3×3 homogeneous transformation matrix which has a special structure. Try your hand at some online MATLAB problems. You’ll need to watch all the 2D “Spatial Maths” lessons to complete the problem set.

Imagine trying to find a face in a crowd. If we know what the face looks like we could search for it at every possible location — this is the essence of template matching. To make it work we need to describe how similar each area we are checking is to the reference face image […]

Most computers today have a built-in camera. Let’s look at how we can grab images directly from such a camera and put them in the MATLAB workspace.